Ange Postecoglou's side moved to eighth in the table with 10 points, while United, now in 12th with seven points, struggled after captain Bruno Fernandes was sent off in the 42nd minute for a high challenge.
Spurs opened the scoring early when Micky van de Ven's run set up Johnson for an easy tap-in. They doubled their lead just after halftime when Johnson's deflected cross found Kulusevski, who scored with a clever flick. Solanke sealed the win in the 77th minute, tapping in from close range after a corner, sending frustrated United fans heading for the exits.